the thought was born with a fellow collector who owns a multi-signed book , with multiple signatures of the same author and now I am just curious to get your opinions on that case.

When you follow the "signed book" situation way back in history,
in the very first days owning a signed book meant that this was a gift from the author to you as a person, nearly close to 100% of the cases with an inscription of dedication.

Other then that signed books where not known.

With growing size of literature and writers, and also with the fame of particular writers
signing a book translates (for me) to "the Author had this particular book in hands , and the sig proofes that" or "i met the author in person"

when you follow this thesis, and i would be curious to hear if you do, what would that mean for multi signed works ?

does having multiple signatures of one author in one book makes a difference to you ?
What does a signature mean to you ?